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粗糙表面是由大量无规则的面元组成的,当用长相干的激光照射物体表面时,不同的面元对相干光反射或者散射形成不同的光程差,这些反射或者散射光的子波在空间中相互干渉,在物体表面形成随机分布的亮点与暗点,这些亮暗相间的点就是激光散斑。让光经过光学系统,在物体表面形成的散斑称为主观散斑。主观散斑原理如图 1a所示,激光散斑如图 1b所示[17-18]。
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数字图像相关法最开始由美国的PETERS和日本的YAMAGUCH在20世纪80年代初分别提出[19-20],该方法处理的是变形前后试件表面的散斑图像,图 2所示为其基本原图。在参考图像f(x,y)中取以某点(x0,y0)为中心(2M+1)×(2M+1)像素大小的正方形参考图像子区,在变形后图像g(x′,y′)中通过亚像素搜索的方法按定义的相关函数来进行相关计算,在变形后图像中寻找与参考图像子区的相关系数最大值的以(x′0,y′0)为中心的区域,即目标子区。根据目标子区分别确定参考图像子区中心点(x0,y0)的x方向和y方向的位移分量u,v。对全部子区进行相关计算,就可以获得全场变形信息。
将变形前后图像子区间的相似度量函数定义为相关函数,目前主要应用的是零均值归一化互相关函数(zero mean normalized cross correlation function,ZNCC)[21]:
$ \begin{array}{*{20}{c}} & C_{\mathrm{ZNCC}}= \\ & \sum\limits_{x=-M}^M \sum\limits_{y=-M}^M\left\{[f(x, y)-\bar{f}] \times\left[g\left(x^{\prime}, y^{\prime}\right)-\bar{g}\right]\right\} \\ & \sqrt{\sum\limits_{x=-M}^M \sum\limits_{y=-M}^M[f(x, y)-\bar{f}]^2} \sqrt{\sum\limits_{x=-M}^M \sum\limits_{y=-M}^M\left[g\left(x^{\prime}, y^{\prime}\right)-\bar{g}\right]^2} \\ & \end{array} $
(1) 式中,f(x,y)为参考图像点(x0,y0)的灰度值,g(x′,y′)为变形后图像点(x′0,y′0)处的灰度值;f=(2M+1)-2$\sum\limits_{x=-M}^M \sum\limits_{y=-M}^M f(x, y)$和g=(2M+1)-2$\sum\limits_{x=-M}^M \sum\limits_{y=-M}^M g(x', y')$分别为参考图像和变形后图像,大小为(2M+1)×(2M+1)的子区的平均灰度值。
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图 5a与图 5b分别是在非真空条件下人工散斑与激光散斑DIC法测得的铝试件应变结果。图中exx和eyy分别代表x方向与y方向的热应变随升温时间的变化曲线。对比人工散斑与激光散斑的结果,两者热应变的变化趋势基本一致,其中激光散斑计算得到的应变结果绝对值略小于人工散斑。分析误差来源,可能是由于管式炉的非真空加热过程是开放式的,两次加热实验的试件温升曲线受环境温度影响较大,导致试件实际的温度变化曲线有差别。此外,相比于人工散斑,激光散斑的应变曲线出现了明显的抖动,这是由于在高温非真空环境下,空气温度分布不均匀造成热流扰动,使得试件表面附近的空气折射率发生变化,从而导致激光散斑图像出现抖动,降低了DIC计算时的图像相关性。因此,在使用激光散斑作为特征、用数字图像相关法计算热应变时,应尽量采用真空环境,避免空气热流扰动带来的计算误差。实验工况无法实现真空环境时,需要采用平滑算法修正,减小应变曲线的波动[13]。
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为了去除热流扰动影响,分别在管式加热炉中对人工散斑与激光散斑的铝(Al)块试件进行真空加热。在加热过程中以1张/5 s的帧率采集550张散斑图,并对散斑图用PMLAB DIC软件进行计算,对获取的x方向和y方向应变曲线取平均值。人工散斑结果如图 6a中所示,激光散斑如图 6b所示。根据管式炉设备显示,温度随时间变化如图 6c所示。将获取的人工散斑和激光散斑平均应变曲线进行比较,如图 6d所示。
根据图 6所示,铝试件真空加热实验的人工散斑与激光散斑热应变曲线都比较光滑,并且都呈现较好的金属各向同性,特别是激光散斑热应变曲线相比于非真空加热工况下的实验结果,曲线波动的噪声大大降低,计算精度也大大提高。表 1和表 2中分别是x和y方向上激光散斑热应变相比于人工散斑的绝对值差值百分比。
表 1 真空下铝试件热应变exx误差
Table 1. Aluminum test piece under vacuum error of thermal strain exx
time/s artificial speckle
exx/μεlaser speckle
exx/μεerror/% 500 724.29 602.75 16.78 750 1159.44 1056.07 8.92 1000 1778.27 1658.66 6.72 1500 3918.26 3818.12 2.56 2000 6458.03 6785.45 5.07 2500 9136.75 9571.47 4.76 2750 10177.89 10885.16 6.95 表 2 真空下铝试件热应变eyy误差
Table 2. Aluminum test piece under vacuum error of thermal strain eyy
time/s artificial speckle
eyy/μεlaser speckle
eyy/μεerror/% 500 638.70 564.81 11.57 750 1028.67 1160.37 12.8 1000 1739.87 1889.55 8.61 1500 3725.88 4038.33 8.39 2000 6306.47 6704.35 6.31 2500 9023.73 9495.82 5.23 2750 10178.13 10809.03 6.20 根据表 1和表 2所示,铝试件在应变低于1200 με左右时,激光散斑与人工散斑计算结果相差较大;当应变值达到1200 με以上时,两者相差基本在10%以内。存在误差的主要原因有两个:(1)管式炉加热铝试件的设备并不能保证每次实验的温升曲线都完全重合,人工散斑和激光散斑两次实验的试件实际温度变化曲线本身就存在误差,导致图 6a和图 6b中的热应变计算结果存在一个差值;(2)当试件温度较低时,热应变也比较小,DIC法在测量微小应变时的计算误差相对较大,但两种实验方法计算得到的热应变曲线基本一致,都能较好的反应出试件的热应变变化性能。
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为了考察激光散斑DIC法能否用于检测托卡马克装置中偏滤器钨(W)靶板受热流冲击产生的热应变,本文中在管式加热炉中分别对人工散斑与激光散斑的钨块试件进行真空加热,在加热过程中,CCD相机以1张/10 s的频率分别采集人工散斑图和激光散斑图各450张。对采集完的图像用PMLAB DIC软件计算并分析,并对获取的x方向应变exx和y方向应变eyy曲线取平均值,获得的人工散斑和激光散斑平均应变曲线分别如图 7a和图 7b所示。根据管式炉设备显示,温度随时间变化如图 7c所示。将获取的人工散斑与激光散斑平均应变曲线进行比较,如图 7d所示。
根据图 7所示,钨试件的热应变同样呈现较好的金属各向同性,取图 7b激光散斑中1000 s,2000 s,3000 s,3500 s,4000 s,4500 s时间处x和y方向上的热应变计算结果,与人工散斑计算得到的热应变量相比较,其绝对值差值百分比如表 3和表 4所示。
表 3 真空下钨试件热应变exx误差
Table 3. Tungsten test piece under vacuum error of thermal strain exx
time/s artificial speckle
exx/μεlaser speckle
exx/μεerror/% 1000 184.45 161.17 12.72 2000 702.67 598.77 14.80 3000 1814.61 1619.90 10.73 3500 2382.81 2301.32 3.42 4000 2979.46 3022.16 1.43 4500 3634.15 3676.24 1.16 表 4 真空下钨试件热应变eyy误差
Table 4. Tungsten test piece under vacuum error of thermal strain eyy
time/s artificial speckle
eyy/μεlaser speckle
eyy/μεerror/% 1000 210.65 174.81 17.01 2000 758.89 619.74 18.33 3000 1885.15 1687.30 10.5 3500 2459.96 2387.57 2.94 4000 3072.52 2950.41 3.97 4500 3717.92 3597.12 3.25 根据表 3和表 4所示,钨试件在应变低于1900 με左右时,激光散斑与人工散斑计算结果相差较大;当应变值达到1900 με以上时,两者相差基本在10%以内。存在误差的主要原因与铝相同:(1)管式炉加热钨试件时试件升温过程并不完全重合,人工散斑和激光散斑两次实验的试件实际温度变化曲线存在误差导致图 7a和图 7b中的热应变计算结果存在一个差值;(2)热应变较小时,DIC法在测量微小应变时的计算噪声会相对较大,且与铝相比,钨的热膨胀系数要小得多,因此需要更高的温度,才会有更大的应变。但两种实验方法计算得到的热应变曲线在高温、大应变条件下,都能较好的反应出钨试件的热应变变化性能。
基于激光散斑数字图像相关法的热应变测量
Thermal strain measurement based on laser speckle digital image correlation method
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摘要: 为了解决常规数字图像相关法应用于高温工况下热应变测量时, 人工制作的散斑受高热载荷冲击容易出现变色、熔化、脱落的问题, 采用激光散斑作为数字图像相关法特征纹理的方法, 计算温度变化前后散斑图像相关性来测量金属热应变, 进行了非真空环境下加热试件的实验, 以及在管式加热炉中分别对铝试件和钨试件进行人工散斑和激光散斑的真空加热实验对比, 取得了相应的散斑图像, 并计算出平均应变曲线数据。结果表明, 在非真空环境下, 由于热流扰动导致激光散斑图像抖动较大, 测量出的热应变曲线存在较大的干扰噪声; 铝从室温升至450 ℃和钨从室温升至800 ℃的热应变与人工散斑结果相对一致; 激光散斑数字图像相关法在类似聚变堆偏滤器高真空、高热流条件下, 可以有效地测出金属壁面的动态热应变。该研究为聚变堆偏滤器第一壁材料的损伤诊断提供了新思路。Abstract: In order to solve the problem of discoloration, melting and falling off of artificial speckles when the conventional digital image correlation method is applied to thermal strain measurement under high temperature conditions, the laser speckle was used as the characteristic texture method of the digital image correlation method. The correlation of speckle images before and after temperature change to measure metal thermal strain was calculated, experiments of heating specimens in a non-vacuum environment were carried out, the artificial speckle and laser tests on aluminum and tungsten specimens in a tubular heating furnace respectively vacuum heating experimental comparison of speckle were conducted.The corresponding speckle images were obtained and the mean strain curve data were calculated. The results show that in the non-vacuum environment, the laser speckle image jitters greatly due to the disturbance of heat flow, and the measured thermal strain curve has large interference noise. The thermal strain of aluminum with the temperature increases from room temperature to 450 ℃ and the thermal strain of tungsten with the temperature increases from room temperature to 800 ℃ is respectively consistent with the artificial speckle results. This study shows that the laser speckle digital image correlation method can effectively measure the dynamic thermal strain of the metal wall under the conditions of high vacuum and high heat flow similar to the fusion reactor divertor, which provides a new idea for the damage diagnosis of the first wall material of the fusion reactor divertor.
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表 1 真空下铝试件热应变exx误差
Table 1. Aluminum test piece under vacuum error of thermal strain exx
time/s artificial speckle
exx/μεlaser speckle
exx/μεerror/% 500 724.29 602.75 16.78 750 1159.44 1056.07 8.92 1000 1778.27 1658.66 6.72 1500 3918.26 3818.12 2.56 2000 6458.03 6785.45 5.07 2500 9136.75 9571.47 4.76 2750 10177.89 10885.16 6.95 表 2 真空下铝试件热应变eyy误差
Table 2. Aluminum test piece under vacuum error of thermal strain eyy
time/s artificial speckle
eyy/μεlaser speckle
eyy/μεerror/% 500 638.70 564.81 11.57 750 1028.67 1160.37 12.8 1000 1739.87 1889.55 8.61 1500 3725.88 4038.33 8.39 2000 6306.47 6704.35 6.31 2500 9023.73 9495.82 5.23 2750 10178.13 10809.03 6.20 表 3 真空下钨试件热应变exx误差
Table 3. Tungsten test piece under vacuum error of thermal strain exx
time/s artificial speckle
exx/μεlaser speckle
exx/μεerror/% 1000 184.45 161.17 12.72 2000 702.67 598.77 14.80 3000 1814.61 1619.90 10.73 3500 2382.81 2301.32 3.42 4000 2979.46 3022.16 1.43 4500 3634.15 3676.24 1.16 表 4 真空下钨试件热应变eyy误差
Table 4. Tungsten test piece under vacuum error of thermal strain eyy
time/s artificial speckle
eyy/μεlaser speckle
eyy/μεerror/% 1000 210.65 174.81 17.01 2000 758.89 619.74 18.33 3000 1885.15 1687.30 10.5 3500 2459.96 2387.57 2.94 4000 3072.52 2950.41 3.97 4500 3717.92 3597.12 3.25 -
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